Mathematics

14 pages, 1165 KiB

Open AccessArticle

A Differential Flatness-Based Model Predictive Control Strategy for a Nonlinear Quarter-Car Active Suspension System

by Daniel Rodriguez-Guevara, Antonio Favela-Contreras, Francisco Beltran-Carbajal, Carlos Sotelo and David Sotelo

Mathematics 2023, 11(4), 1067; https://doi.org/10.3390/math11041067 - 20 Feb 2023

Cited by 1 | Viewed by 1386

Abstract

Controlling an automotive suspension system using an actuator is a complex nonlinear problem that requires both fast and precise solutions in order to achieve optimal performance. In this work, the nonlinear model of a quarter-car active suspension is expressed in terms of a [...] Read more.

Controlling an automotive suspension system using an actuator is a complex nonlinear problem that requires both fast and precise solutions in order to achieve optimal performance. In this work, the nonlinear model of a quarter-car active suspension is expressed in terms of a flat output and its derivatives in order to embed the nonlinearities of the system in the flat output. Afterward, a Model Predictive Controller based on the differential flatness derivation (MPC-DF) of the quarter-car is proposed in order to achieve optimal control performance in both passenger comfort and road holding without diminishing the lifespan of the wheel. This formulation results in a linear optimization problem while maintaining the nonlinear behavior of the active suspension system. Afterward, the optimization problem is solved by means of Quadratic Programming (QP), enabling real-time implementation. Simulation results are presented using a realistic road disturbance to show the effectiveness of the proposed control strategy. Full article

(This article belongs to the Special Issue Mathematical Methods for Nonlinear Control)

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26 pages, 1558 KiB

Open AccessArticle

Global Stability of a MERS-CoV Infection Model with CTL Immune Response and Intracellular Delay

by Tuersunjiang Keyoumu, Wanbiao Ma and Ke Guo

Mathematics 2023, 11(4), 1066; https://doi.org/10.3390/math11041066 - 20 Feb 2023

Cited by 3 | Viewed by 1112

Abstract

In this paper, we propose and study a Middle East respiratory syndrome coronavirus (MERS-CoV) infection model with cytotoxic T lymphocyte (CTL) immune response and intracellular delay. This model includes five compartments: uninfected cells, infected cells, viruses, dipeptidyl peptidase 4 (DPP4), and CTL immune [...] Read more.

In this paper, we propose and study a Middle East respiratory syndrome coronavirus (MERS-CoV) infection model with cytotoxic T lymphocyte (CTL) immune response and intracellular delay. This model includes five compartments: uninfected cells, infected cells, viruses, dipeptidyl peptidase 4 (DPP4), and CTL immune cells. We obtained an immunity-inactivated reproduction number

R_{0}

and an immunity-activated reproduction number

R_{1}

. By analyzing the distributions of roots of the corresponding characteristic equations, the local stability results of the infection-free equilibrium, the immunity-inactivated equilibrium, and the immunity-activated equilibrium were obtained. Moreover, by constructing suitable Lyapunov functionals and combining LaSalle’s invariance principle and Barbalat’s lemma, some sufficient conditions for the global stability of the three types of equilibria were obtained. It was found that the infection-free equilibrium is globally asymptotically stable if

R_{0} \leq 1

and unstable if

R_{0} > 1

; the immunity-inactivated equilibrium is locally asymptotically stable if

R_{0} > 1 > R_{1}

and globally asymptotically stable if

R_{0} > 1 > R_{1}

and condition (H1) holds, but unstable if

R_{1} > 1

; and the immunity-activated equilibrium is locally asymptotically stable if

R_{1} > 1

and is globally asymptotically stable if

R_{1} > 1

and condition (H1) holds. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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17 pages, 315 KiB

Open AccessArticle

Optimal Stopping and Loading Rules Considering Multiple Attempts and Task Success Criteria

by Yaguang Wu

Mathematics 2023, 11(4), 1065; https://doi.org/10.3390/math11041065 - 20 Feb 2023

Cited by 1 | Viewed by 801

Abstract

Numerous engineering systems gradually deteriorate due to internal stress caused by the working load. The system deterioration process is directly related to the workload, providing opportunities for decision-makers to manage system deterioration by modifying the workload. As one of the most effective ways [...] Read more.

Numerous engineering systems gradually deteriorate due to internal stress caused by the working load. The system deterioration process is directly related to the workload, providing opportunities for decision-makers to manage system deterioration by modifying the workload. As one of the most effective ways to control system malfunction risk, mission stopping has been extensively studied. Most existing research on mission stopping ignores the effect of working loads on the internal deterioration of safety-critical systems. The purpose of this work is to examine the optimal joint loading and stopping rules for systems subject to internal degradation under two types of mission success requirements (MSR). The problem is formulated using the recursive algorithm to minimize the expected cost over the mission. Mission reliability and system safety are assessed, and the optimal loading and stopping rules are investigated. The established models are illustrated by practical examples, and comprehensive policy comparison and parameter sensitivity analysis on the allowable mission time, mission duration and the number of mission tries are conducted. Our findings indicate that dynamic load level modification has a substantial effect on system deterioration and predicted long-term costs. For the purpose of decision-making, several managerial implications for the joint development of load adjustment and abort implementation are obtained. Full article

(This article belongs to the Special Issue System Reliability and Quality Management in Industrial Engineering)

21 pages, 2850 KiB

Open AccessArticle

Modified Finite Element Study for Heat and Mass Transfer of Electrical MHD Non-Newtonian Boundary Layer Nanofluid Flow

by Muhammad Shoaib Arif, Wasfi Shatanawi and Yasir Nawaz

Mathematics 2023, 11(4), 1064; https://doi.org/10.3390/math11041064 - 20 Feb 2023

Cited by 4 | Viewed by 1449

Abstract

Research into the effects of different parameters on flow phenomena is necessary due to the wide range of potential applications of non-Newtonian boundary layer nanofluid flow, including but not limited to production industries, polymer processing, compression, power generation, lubrication systems, food manufacturing, and [...] Read more.

Research into the effects of different parameters on flow phenomena is necessary due to the wide range of potential applications of non-Newtonian boundary layer nanofluid flow, including but not limited to production industries, polymer processing, compression, power generation, lubrication systems, food manufacturing, and air conditioning. Because of this impetus, we investigated non-Newtonian fluid flow regimes from the perspectives of both heat and mass transfer aspects. In this study, heat transfer of electrical MHD non-Newtonian flow of Casson nanofluid over the flat plate is investigated under the effects of variable thermal conductivity and mass diffusivity. Emerging problems occur as nonlinear partial differential equations (NPDEs) in opposition to the conservation laws of mass, momentum, heat, and species transportation. The shown problem can be recast as a set of ordinary differential equations by making the necessary changes. A modified finite element method is adopted to solve the obtained set of ODEs. The numerical method is based on Galerkin weighted residual approach, and Gauss–Legendre numerical integration is adopted in the modified finite element method application procedure. To clarify the obtained results, another numerical technique is employed to solve the reduced ODEs. With the help of error tables and the flowing behavior of complicated physical parameters on estimated solutions, this study graphically and tabulatively explains the convergence of analytic solutions. Comparing some of the obtained results with those given in past research is also done. From the obtained results, it is observed that the velocity profile escalates by improving the electric parameter. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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44 pages, 525 KiB

Open AccessArticle

Integrable Systems: In the Footprints of the Greats

by Velimir Jurdjevic

Mathematics 2023, 11(4), 1063; https://doi.org/10.3390/math11041063 - 20 Feb 2023

Cited by 1 | Viewed by 920

Abstract

In his 1842 lectures on dynamics C.G. Jacobi summarized difficulties with differential equations by saying that the main problem in the integration of differential equations appears in the choice of right variables. Since there is no general rule for finding the right choice, [...] Read more.

In his 1842 lectures on dynamics C.G. Jacobi summarized difficulties with differential equations by saying that the main problem in the integration of differential equations appears in the choice of right variables. Since there is no general rule for finding the right choice, it is better to introduce special variables first, and then investigate the problems that naturally lend themselves to these variables. This paper follows Jacobi’s prophetic observations by introducing certain “meta” variational problems on semi-simple reductive groups G having a compact subgroup K. We then use the Maximum Principle of optimal control to generate the Hamiltonians whose solutions project onto the extremal curves of these problems. We show that there is a particular sub-class of these Hamiltonians that admit a spectral representation on the Lie algebra of G. As a consequence, the spectral invariants associated with the spectral curve produce a large number of integrals of motion, all in involution with each other, that often meet the Liouville complete integrability criteria. We then show that the classical integrals of motion associated, with the Kowalewski top, the two-body problem of Kepler, and Jacobi’s geodesic problem on the ellipsoid can be all derived from the aforementioned Hamiltonian systems. We also introduce a rolling geodesic problem that admits a spectral representation on symmetric Riemannian spaces and we then show the relevance of the corresponding integrals on the nature of the curves whose elastic energy is minimal. Full article

(This article belongs to the Special Issue Completely Integrable Equations: Algebraic Aspects and Applications)

16 pages, 325 KiB

Open AccessArticle

Remarks on the “Onsager Singularity Theorem” for Leray–Hopf Weak Solutions: The Hölder Continuous Case

by Luigi C. Berselli

Mathematics 2023, 11(4), 1062; https://doi.org/10.3390/math11041062 - 20 Feb 2023

Cited by 2 | Viewed by 891

Abstract

In this paper, we first present an overview of the results related to energy conservation in spaces of Hölder-continuous functions for weak solutions to the Euler and Navier–Stokes equations. We then consider families of weak solutions to the Navier–Stokes equations with Hölder-continuous velocities [...] Read more.

In this paper, we first present an overview of the results related to energy conservation in spaces of Hölder-continuous functions for weak solutions to the Euler and Navier–Stokes equations. We then consider families of weak solutions to the Navier–Stokes equations with Hölder-continuous velocities with norms uniformly bound in terms of viscosity. We finally provide the proofs of our original results that extend the range of allowed exponents for inviscid limits producing solutions to the Euler equations satisfying the energy equality, and improve the so-called “Onsager singularity” theorem. Full article

(This article belongs to the Special Issue Mathematical Dynamic Flow Models)

17 pages, 361 KiB

Open AccessArticle

Associated Statistical Parameters’ Aggregations in Interactive MADM

by Gia Sirbiladze and Tariel Khvedelidze

Mathematics 2023, 11(4), 1061; https://doi.org/10.3390/math11041061 - 20 Feb 2023

Viewed by 736

Abstract

From recent studies, the concept of “monotone expectation” (ME) of Interactive Multi-Attribute Decision Making (MADM) is well known, which was developed for the case of different fuzzy sets. This article develops the concept of “monotone expectation” for such statistical parameters as variance,

k

[...] Read more.

From recent studies, the concept of “monotone expectation” (ME) of Interactive Multi-Attribute Decision Making (MADM) is well known, which was developed for the case of different fuzzy sets. This article develops the concept of “monotone expectation” for such statistical parameters as variance,

k

-order moment and covariance. We investigate the problem of the definition of some statistical parameters, when the uncertainty is represented by a monotone measure—a fuzzy measure—instead of an additive measure. The study presents the concept of the definition of monotone statistical parameters based on the Choquet finite integral for the definition of monotone expectation, monotone variance, monotone

k

-order moment and monotone covariance. Associated statistical parameters are also presented—expectation, variance,

k

-order moment and covariance—which are defined in relation to associated probabilities of a fuzzy measure. It is shown that the monotone statistical parameters defined in the study are defined by one particular relevant associated statistical parameter out of the total number

n!

of such parameters. It is also shown that the aggregations with monotone statistical parameters used in interactive MADM models take into account interactions of the focal elements of only one consonant structure from the

n!

consonant structures of attributes. In order to take into account the interactions of the focal elements of all

n!

consonant structures of attributes, the monotone statistical parameters were expanded into the

F

-associated statistical parameters. Expansion correctness implies that if dual second-order Choquet capacities are taken as the fuzzy measures of aggregation of the

F

-associated statistical parameters, then the

F

-associated statistical parameters coincide with the corresponding monotone statistical parameters. A scheme for embedding new aggregation operators, monotone statistical parameters and

F

-associated statistical parameters into the interactive MADM model has been developed. Specific numerical examples are presented to illustrate the obtained results. Full article

(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)

17 pages, 400 KiB

Open AccessArticle

New Results Involving the Generalized Krätzel Function with Application to the Fractional Kinetic Equations

by Asifa Tassaddiq and Rekha Srivastava

Mathematics 2023, 11(4), 1060; https://doi.org/10.3390/math11041060 - 20 Feb 2023

Cited by 4 | Viewed by 992

Abstract

Sun is a basic component of the natural environment and kinetic equations are important mathematical models to assess the rate of change of chemical composition of a star such as the sun. In this article, a new fractional kinetic equation is formulated and [...] Read more.

Sun is a basic component of the natural environment and kinetic equations are important mathematical models to assess the rate of change of chemical composition of a star such as the sun. In this article, a new fractional kinetic equation is formulated and solved using generalized Krätzel integrals because the nuclear reaction rate in astrophysics is represented in terms of these integrals. Furthermore, new identities involving Fox–Wright function are discussed and used to simplify the results. We compute new fractional calculus formulae involving the Krätzel function by using Kiryakova’s fractional integral and derivative operators which led to several new identities for a variety of other classic fractional transforms. A number of new identities for the generalized Krätzel function are then analyzed in relation to the

H

-function. The closed form of such results is also expressible in terms of Mittag-Leffler function. Distributional representation of Krätzel function and its Laplace transform has been essential in achieving the goals of this work. Full article

20 pages, 5010 KiB

Open AccessArticle

Fast Single-Parameter Energy Function Thresholding for Image Segmentation Based on Region Information

by Rong Lan, Danlin Feng, Feng Zhao, Jiulun Fan and Haiyan Yu

Mathematics 2023, 11(4), 1059; https://doi.org/10.3390/math11041059 - 20 Feb 2023

Viewed by 1301

Abstract

To solve the problems of image threshold segmentation based on weak continuous constraint theory, the running time is long, and the two parameters need to be selected manually, and therefore a fast single-parameter energy function thresholding for image segmentation based on region information [...] Read more.

To solve the problems of image threshold segmentation based on weak continuous constraint theory, the running time is long, and the two parameters need to be selected manually, and therefore a fast single-parameter energy function thresholding for image segmentation based on region information (FSEFTISRI) is proposed in this paper. The proposed FSEFTISRI algorithm uses simple linear iterative clustering (SLIC) technology to pre-block the image, extract the image super-pixels, and then map the image super-pixels to the interval type-2 fuzzy set (IT2FS), so as to construct the single-parameter energy function to search the optimal threshold, and adaptively select the penalty parameters in the energy function through the class uncertainty theory. On a non-destructive testing (NDT) database and Berkeley segmentation datasets and benchmarks (BSDS), the proposed FSEFTISRI is compared with five related algorithms. The average misclassification error (ME) of the proposed FSEFTISRI algorithm on NDT and BSDS are 0.0466 and 0.0039, respectively. The results show that the proposed FSEFTISRI has acquired more satisfactory results in visual effect and evaluation index, and the running time of the proposed FSEFTISRI algorithm is shorter, which shows the effectiveness of the proposed FSEFTISRI. Full article

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12 pages, 278 KiB

Open AccessArticle

Risk-Sensitive Maximum Principle for Controlled System with Delay

by Peng Wang

Mathematics 2023, 11(4), 1058; https://doi.org/10.3390/math11041058 - 20 Feb 2023

Cited by 1 | Viewed by 832

Abstract

Risk-sensitive maximum principle and verification theorem for controlled system with delay is obtained by virtue of classical convex variational technique. The prime feature in the research is that risk-sensitive parameter

ϑ

seriously affects adjoint equation and variational inequality. Moreover, a verification theorem of [...] Read more.

Risk-sensitive maximum principle and verification theorem for controlled system with delay is obtained by virtue of classical convex variational technique. The prime feature in the research is that risk-sensitive parameter

ϑ

seriously affects adjoint equation and variational inequality. Moreover, a verification theorem of optimality is derived under some concavity conditions. An example is given to illustrate our theoretical result. Full article

(This article belongs to the Section Computational and Applied Mathematics)

27 pages, 14004 KiB

Open AccessArticle

Numerical Study of a Phase Change Material Energy Storage Tank Working with Carbon Nanotube–Water Nanofluid under Ha’il City Climatic Conditions

by Lioua Kolsi, Ahmed Kadhim Hussein, Walid Hassen, Lotfi Ben Said, Badreddine Ayadi, Wajdi Rajhi, Taher Labidi, Ali Shawabkeh and Katta Ramesh

Mathematics 2023, 11(4), 1057; https://doi.org/10.3390/math11041057 - 20 Feb 2023

Cited by 14 | Viewed by 1666

Abstract

A numerical investigation of a phase change material (PCM) energy storage tank working with carbon nanotube (CNT)–water nanofluid is performed. The study was conducted under actual climatic conditions of the Ha’il region (Saudi Arabia). Two configurations related to the absence or presence of [...] Read more.

A numerical investigation of a phase change material (PCM) energy storage tank working with carbon nanotube (CNT)–water nanofluid is performed. The study was conducted under actual climatic conditions of the Ha’il region (Saudi Arabia). Two configurations related to the absence or presence of conductive baffles are studied. The tank is filled by encapsulated paraffin wax as the PCM, and CNT–water nanofluid flows through the capsules. The main goal is to increase the temperature of the PCM to 70 °C in order to store the thermal energy, which can then be used during the night and cloudy weather. Numerical computations are made using the finite element method (FEM) based on actual measured weather conditions. Climate conditions were collected from a weather station located on the roof of the engineering college’s building at the University of Ha’il. The collected data served as input to the numerical model, and the simulations were performed for three months (December, March, and July). The solid CNT volume fraction range was (0 ≤ ϕ ≤ 0.05) and the nanofluid volume flow rate ranged was (0.5 L/min ≤ V ≤ 3 L/min). For both considered cases (with and without baffles), it was found that the use of CNT–nanofluid led to a reduction in the charging time and enhanced its performance. An increase in the volumetric flow rate was found to accelerate the melting process. The best performances of the storage tank occurred during July due to the highest solar irradiation. Furthermore, it was found that the use of baffles had no beneficial effects on the melting process. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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9 pages, 612 KiB

Open AccessArticle

Algebraic Methods for Achieving Super-Resolution by Digital Antenna Arrays

by Boris A. Lagovsky and Evgeny Ya. Rubinovich

Mathematics 2023, 11(4), 1056; https://doi.org/10.3390/math11041056 - 20 Feb 2023

Cited by 2 | Viewed by 1029

Abstract

The actual modern problem of developing and improving measurement and observation systems (including robotic ones) is to increase the volume and quality of the information received. Increasing the angle resolution to values significantly exceeding the Rayleigh criterion, i.e. achieving super-resolution is one of [...] Read more.

The actual modern problem of developing and improving measurement and observation systems (including robotic ones) is to increase the volume and quality of the information received. Increasing the angle resolution to values significantly exceeding the Rayleigh criterion, i.e. achieving super-resolution is one of important ways to solve the problem. Angular super-resolution which makes it possible to detail images of research objects and their individual fragments, improves the quality of solutions to detection, recognition and identification problems, increases the range of such systems. In many papers methods developed by authors to achieve a super-resolution based on approximate solutions of inverse problems in the form of Fredholm integral equation of the first kind of convolution type called algebraic are presented. The methods used, as well as their varieties, make it possible to reduce solutions of inverse problems posed to solving sets of linear algebraic equations (SLAE). This paper presents results of further improvement of algebraic methods based on intelligent analysis of received signals. It is shown that their use in systems based on digital antenna arrays makes it possible to increase the achieved degree of exceeding the Rayleigh criterion. In the course of numerical experiments with a mathematical model, the stability of the solutions obtained and their adequacy were confirmed. The numerical results obtained open the following possibilities: (1) obtaining images of studied objects with a resolution exceeding the Rayleigh criterion by 4 to 10 times, (2) determining the angular coordinates of individual small-sized objects as part of multi-element complex objects (group targets), (3) clarifying boundaries of extended objects and their individual elements, (4) localizing individual bright objects on a smoothly inhomogeneous reflective background. Applying presented new methods does not require a significant computing power, what allows you to work in a real time mode using relatively simple and inexpensive computing devices. The ways of further improvement of presented algebraic methods for solving applied inverse problems are described. Full article

(This article belongs to the Special Issue Dynamics and Control Theory with Applications)

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13 pages, 508 KiB

Open AccessReview

Programming for High-Performance Computing on Edge Accelerators

by Pilsung Kang

Mathematics 2023, 11(4), 1055; https://doi.org/10.3390/math11041055 - 20 Feb 2023

Cited by 4 | Viewed by 2150

Abstract

The field of edge computing has grown considerably over the past few years, with applications in artificial intelligence and big data processing, particularly due to its powerful accelerators offering a large amount of hardware parallelism. As the computing power of the latest edge [...] Read more.

The field of edge computing has grown considerably over the past few years, with applications in artificial intelligence and big data processing, particularly due to its powerful accelerators offering a large amount of hardware parallelism. As the computing power of the latest edge systems increases, applications of edge computing are being expanded to areas that have traditionally required substantially high-performant computing resources such as scientific computing. In this paper, we review the latest literature and present the current status of research for implementing high-performance computing (HPC) on edge devices equipped with parallel accelerators, focusing on software environments including programming models and benchmark methods. We also examine the applicability of existing approaches and discuss possible improvements necessary towards realizing HPC on modern edge systems. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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15 pages, 1107 KiB

Open AccessArticle

Financial Time Series Forecasting with the Deep Learning Ensemble Model

by Kaijian He, Qian Yang, Lei Ji, Jingcheng Pan and Yingchao Zou

Mathematics 2023, 11(4), 1054; https://doi.org/10.3390/math11041054 - 20 Feb 2023

Cited by 19 | Viewed by 10035

Abstract

With the continuous development of financial markets worldwide to tackle rapid changes such as climate change and global warming, there has been increasing recognition of the importance of financial time series forecasting in financial market operation and management. In this paper, we propose [...] Read more.

With the continuous development of financial markets worldwide to tackle rapid changes such as climate change and global warming, there has been increasing recognition of the importance of financial time series forecasting in financial market operation and management. In this paper, we propose a new financial time series forecasting model based on the deep learning ensemble model. The model is constructed by taking advantage of a convolutional neural network (CNN), long short-term memory (LSTM) network, and the autoregressive moving average (ARMA) model. The CNN-LSTM model is introduced to model the spatiotemporal data feature, while the ARMA model is used to model the autocorrelation data feature. These models are combined in the ensemble framework to model the mixture of linear and nonlinear data features in the financial time series. The empirical results using financial time series data show that the proposed deep learning ensemble-based financial time series forecasting model achieved superior performance in terms of forecasting accuracy and robustness compared with the benchmark individual models. Full article

(This article belongs to the Special Issue Mathematical Modeling and Machine Learning with Application to Economics and Finance)

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17 pages, 2859 KiB

Open AccessArticle

Comparing Friends and Peer Tutors Amidst COVID-19 Using Social Network Analysis

by Nurul Zahirah Abd Rahim, Nurun Najwa Bahari, Nur Syaza Mohd Azzimi, Zamira Hasanah Zamzuri, Hafizah Bahaludin, Nurul Farahain Mohammad and Fatimah Abdul Razak

Mathematics 2023, 11(4), 1053; https://doi.org/10.3390/math11041053 - 20 Feb 2023

Viewed by 1639

Abstract

COVID-19 has drastically changed the teaching patterns of higher education from face-to-face to online learning, and it has also affected students’ engagement socially and academically. Understanding the nature of students’ engagement during online learning can help in identifying related issues so that various [...] Read more.

COVID-19 has drastically changed the teaching patterns of higher education from face-to-face to online learning, and it has also affected students’ engagement socially and academically. Understanding the nature of students’ engagement during online learning can help in identifying related issues so that various initiatives can be implemented in adapting to this situation. In this study, social network analysis is conducted to gain insights on students’ engagement during COVID-19. Directed and weighted networks were used to visualize and analyze friendship as well as peer tutor networks obtained from online questionnaires answered by all students in the class. Contrasting friends and peer tutors reveals some hidden interactions between students and shines some light on dynamics of the online learning community. The results indicate that, popular and important peer tutors may not be high achievers and thus possibly contributing to the spread of misinformation in the online learning community. By comparing weighted indegree and betweenness centrality values, we suggest approaches to cultivate a healthy online learning community. This study highlights the use of social network analysis to assist and monitor students’ engagement and further formulate strategies in order to make the class a conducive online learning community, particularly in the advent of online learning in higher education institutions. Full article

(This article belongs to the Special Issue Applications of Data Mining Algorithms and Big Data Analytics in Education)

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28 pages, 4953 KiB

Open AccessArticle

A Dynamic Spatio-Temporal Stochastic Modeling Approach of Emergency Calls in an Urban Context

by David Payares-Garcia, Javier Platero and Jorge Mateu

Mathematics 2023, 11(4), 1052; https://doi.org/10.3390/math11041052 - 19 Feb 2023

Viewed by 1423

Abstract

Emergency calls are defined by an ever-expanding utilisation of information and sensing technology, leading to extensive volumes of spatio-temporal high-resolution data. The spatial and temporal character of the emergency calls is leveraged by authorities to allocate resources and infrastructure for an effective response, [...] Read more.

Emergency calls are defined by an ever-expanding utilisation of information and sensing technology, leading to extensive volumes of spatio-temporal high-resolution data. The spatial and temporal character of the emergency calls is leveraged by authorities to allocate resources and infrastructure for an effective response, to identify high-risk event areas, and to develop contingency strategies. In this context, the spatio-temporal analysis of emergency calls is crucial to understanding and mitigating distress situations. However, modelling and predicting crime-related emergency calls remain challenging due to their heterogeneous and dynamic nature with complex underlying processes. In this context, we propose a modelling strategy that accounts for the intrinsic complex space–time dynamics of some crime data on cities by handling complex advection, diffusion, relocation, and volatility processes. This study presents a predictive framework capable of assimilating data and providing confidence estimates on the predictions. By analysing the dynamics of the weekly number of emergency calls in Valencia, Spain, for ten years (2010–2020), we aim to understand and forecast the spatio-temporal behaviour of emergency calls in an urban environment. We include putative geographical variables, as well as distances to relevant city landmarks, into the spatio-temporal point process modelling framework to measure the effect deterministic components exert on the intensity of emergency calls in Valencia. Our results show how landmarks attract or repel offenders and act as proxies to identify areas with high or low emergency calls. We are also able to estimate the weekly average growth and decay in space and time of the emergency calls. Our proposal is intended to guide mitigation strategies and policy. Full article

(This article belongs to the Special Issue Applied Statistical Modeling and Data Mining)

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19 pages, 4641 KiB

Open AccessArticle

Intelligent Health Care and Diseases Management System: Multi-Day-Ahead Predictions of COVID-19

by Ahed Abugabah and Farah Shahid

Mathematics 2023, 11(4), 1051; https://doi.org/10.3390/math11041051 - 19 Feb 2023

Cited by 1 | Viewed by 1131

Abstract

The rapidly growing number of COVID-19 infected and death cases has had a catastrophic worldwide impact. As a case study, the total number of death cases in Algeria is over two thousand people (increased with time), which drives us to search its possible [...] Read more.

The rapidly growing number of COVID-19 infected and death cases has had a catastrophic worldwide impact. As a case study, the total number of death cases in Algeria is over two thousand people (increased with time), which drives us to search its possible trend for early warning and control. In this paper, the proposed model for making a time-series forecast for daily and total infected cases, death cases, and recovered cases for the countrywide Algeria COVID-19 dataset is a two-layer dropout gated recurrent unit (TDGRU). Four performance parameters were used to assess the model’s performance: mean absolute error (MAE), root mean squared error (RMSE), R

^{2}

, and mean absolute percentage error (MAPE). The results generated with TDGRU are compared with actual numbers as well as predictions with conventional time-series techniques, such as autoregressive integrated moving average (ARIMA), machine learning model of linear regression (LR), and the time series-based deep learning method of long short-term memory (LSTM). The experiment results on different time horizons show that the TDGRU model outperforms the other forecasting methods that deliver correct predictions with lower prediction errors. Furthermore, since this TDGRU is based on a relatively simpler architecture than the LSTM, in comparison to LSTM-based models, it features a significantly reduced number of parameters, a shorter training period, a lower memory storage need, and a more straightforward hardware implementation. Full article

(This article belongs to the Topic Engineering Mathematics)

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16 pages, 7147 KiB

Open AccessArticle

Hybrid Traffic Accident Classification Models

by Yihang Zhang and Yunsick Sung

Mathematics 2023, 11(4), 1050; https://doi.org/10.3390/math11041050 - 19 Feb 2023

Cited by 1 | Viewed by 1555

Abstract

Traffic closed-circuit television (CCTV) devices can be used to detect and track objects on roads by designing and applying artificial intelligence and deep learning models. However, extracting useful information from the detected objects and determining the occurrence of traffic accidents are usually difficult. [...] Read more.

Traffic closed-circuit television (CCTV) devices can be used to detect and track objects on roads by designing and applying artificial intelligence and deep learning models. However, extracting useful information from the detected objects and determining the occurrence of traffic accidents are usually difficult. This paper proposes a CCTV frame-based hybrid traffic accident classification model that enables the identification of whether a frame includes accidents by generating object trajectories. The proposed model utilizes a Vision Transformer (ViT) and a Convolutional Neural Network (CNN) to extract latent representations from each frame and corresponding trajectories. The fusion of frame and trajectory features was performed to improve the traffic accident classification ability of the proposed hybrid method. In the experiments, the Car Accident Detection and Prediction (CADP) dataset was used to train the hybrid model, and the accuracy of the model was approximately 97%. The experimental results indicate that the proposed hybrid method demonstrates an improved classification performance compared to traditional models. Full article

(This article belongs to the Special Issue Artificial Neural Networks: Design and Applications)

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18 pages, 2707 KiB

Open AccessArticle

Non-Identical Inverter Rings as an Entropy Source: NIST-90B-Verified TRNG Architecture on FPGAs for IoT Device Integrity

by Hemalatha Mahalingam, Sivaraman Rethinam, Siva Janakiraman and Amirtharajan Rengarajan

Mathematics 2023, 11(4), 1049; https://doi.org/10.3390/math11041049 - 19 Feb 2023

Cited by 2 | Viewed by 1573

Abstract

True random key generator (TRNG) architectures play a notable role in strengthening information security infrastructure. The development of new entropy sources based on reconfigurable hardware is always in demand, especially for the integrity of devices in IoT applications. TRNGs can be adopted for [...] Read more.

True random key generator (TRNG) architectures play a notable role in strengthening information security infrastructure. The development of new entropy sources based on reconfigurable hardware is always in demand, especially for the integrity of devices in IoT applications. TRNGs can be adopted for generating unique device IDs that form the data network in the IoT. A ring oscillator (RO) is an efficient entropy source which can be implemented on FPGAs or realised as ASIC hardware. This work proposes a non-identical RO array as an entropy source. The TRNG architecture, based on an increasing odd number of inverters per ring, was extensively studied. The various statistical and hardware analyses provided encouraging results for this reliable entropy unit. The suggested device-independent non-identical RO structure was implemented on five different types of FPGA hardware belonging to the Xilinx and Intel families, consuming 13 registers and nearly 15 combinational functions. This TRNG achieved a throughput of 3.5 Mbps. While the emergence of the Gaussian response evaluated true randomness, the NIST 800-90B and NIST 800-22 tests yielded good results in terms of the justification of randomness evolving from the proposed TRNG architecture. Full article

(This article belongs to the Special Issue Recent Advances in Security, Privacy, and Applied Cryptography)

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18 pages, 997 KiB

Open AccessArticle

A Study of Privacy-Preserving Neural Network Prediction Based on Replicated Secret Sharing

by Yanru Zhang and Peng Li

Mathematics 2023, 11(4), 1048; https://doi.org/10.3390/math11041048 - 19 Feb 2023

Viewed by 1018

Abstract

Neural networks have a wide range of promise for image prediction, but in the current setting of neural networks as a service, the data privacy of the parties involved in prediction raises concerns. In this paper, we design and implement a privacy-preserving neural [...] Read more.

Neural networks have a wide range of promise for image prediction, but in the current setting of neural networks as a service, the data privacy of the parties involved in prediction raises concerns. In this paper, we design and implement a privacy-preserving neural network prediction model in the three-party secure computation framework over secret sharing of private data. Secret sharing allows the original data to be split, with each share held by a different party. The parties cannot know the shares owned by the remaining collaborators, and thus the original data can be kept secure. The three parties refer to the client, the service provider and the third server that assist in the computation, which is different from the previous work. Thus, under the definition of semi-honest and malicious security, we design new computation protocols for the building blocks of the neural network based on replicated secret sharing. Experimenting with MNIST dataset on different neural network architectures, our scheme improves 1.3×/1.5× and 7.4×/47.6× in terms of computation time as well as communication cost compared to the Falcon framework under the semi-honest/malicious security, respectively. Full article

(This article belongs to the Special Issue Mathematics, Cryptography, Secret Sharing, Information Hiding and Their Applications)

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13 pages, 285 KiB

Open AccessArticle

On Some Solvable Systems of Some Rational Difference Equations of Third Order

by Khalil S. Al-Basyouni and Elsayed M. Elsayed

Mathematics 2023, 11(4), 1047; https://doi.org/10.3390/math11041047 - 19 Feb 2023

Cited by 3 | Viewed by 1055

Abstract

Our aim in this paper is to obtain formulas for solutions of rational difference equations such as

x_{n + 1} = 1 \pm (x_{n - 1} y_{n}) / (1 - y_{n}),

[...] Read more.

Our aim in this paper is to obtain formulas for solutions of rational difference equations such as

x_{n + 1} = 1 \pm (x_{n - 1} y_{n}) / (1 - y_{n}),

y_{n + 1} = 1 \pm (y_{n - 1} x_{n}) / (1 - x_{n}),

and

x_{n + 1} = 1 \pm (x_{n - 1} y_{n - 2}) / (1 - y_{n}),

y_{n + 1} = 1 \pm (y_{n - 1} x_{n - 2}) / (1 - x_{n}),

where the initial conditions

x_{- 2}

,

x_{- 1}

,

x_{0}

,

y_{- 2}

,

y_{- 1}

,

y_{0}

are non-zero real numbers. In addition, we show that the some of these systems are periodic with different periods. We also verify our theoretical outcomes at the end with some numerical applications and draw it by using some mathematical programs to illustrate the results. Full article

(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2023)

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15 pages, 826 KiB

Open AccessArticle

Mathematical Framework for Mixed Reservation- and Priority-Based Traffic Coexistence in 5G NR Systems

by Daria Ivanova, Yves Adou, Ekaterina Markova, Yuliya Gaidamaka and Konstantin Samouylov

Mathematics 2023, 11(4), 1046; https://doi.org/10.3390/math11041046 - 18 Feb 2023

Cited by 1 | Viewed by 1652

Abstract

Fifth-generation (5G) New Radio (NR) systems are expected to support multiple traffic classes including enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLC), and massive machine-type communications (mMTC) at the same air interface. This functionality is assumed to be implemented by utilizing the network [...] Read more.

Fifth-generation (5G) New Radio (NR) systems are expected to support multiple traffic classes including enhanced mobile broadband (eMBB), ultra-reliable low-latency communications (URLLC), and massive machine-type communications (mMTC) at the same air interface. This functionality is assumed to be implemented by utilizing the network slicing concept. According to the 3rd Generation Partnership Project (3GPP), the efficient support of this feature requires statistical multiplexing and, at the same time, traffic isolation between slices. In this paper, we formulate and solve a mathematical model for a class of Radio Access Network (RAN) slicing algorithms that simultaneously include resource reservation and a priority-based service discipline allowing us to incur fine granularity in the service processes of different traffic aggregates. The system is based on a queueing model and allows parametrization by accounting for the specifics of wireless channel impairments. As metrics of interest, we utilize K-class session drop probability, K-class session pre-emption probability, and system resource utilization. To showcase the capabilities of the model, we also compare performance guarantees provided for URLLC, eMBB, and mMTC traffic when multiplexed over the same NR radio interface. Our results demonstrate that the performance trade-off is dictated by the offered traffic load of the highest priority sessions: (i) when it is small, mixed reservation/priority scheme outperforms the full reservation mechanism; (ii) for overloaded conditions, full reservations provides better traffic isolation. The mixed strategy is beneficial to traffic aggregates with short-lived lightweight sessions, such as URLLC and mMTC, while the reservation only scheme works better for elastic eMBB traffic. The most important feature is that the mixed strategy allows resource utilization to be improved up to 95%, which is 10–15% higher compared to the reservation-only scheme while still providing isolation between traffic types. Full article

(This article belongs to the Section Network Science)

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22 pages, 484 KiB

Open AccessArticle

Robust Statistic Estimation in Constrained Optimal Control Problems of Pollution Accumulation (Part II: Markovian Switchings)

by Beatris Adriana Escobedo-Trujillo, José Daniel López-Barrientos, Carmen Geraldi Higuera-Chan and Francisco Alejandro Alaffita-Hernández

Mathematics 2023, 11(4), 1045; https://doi.org/10.3390/math11041045 - 18 Feb 2023

Cited by 1 | Viewed by 987

Abstract

This piece is a follow-up of the research started by the authors on the constrained optimal control problem applied to pollution accumulation. We consider a dynamic system governed by a diffusion process with multiple modes that depends on an unknown parameter. We will [...] Read more.

This piece is a follow-up of the research started by the authors on the constrained optimal control problem applied to pollution accumulation. We consider a dynamic system governed by a diffusion process with multiple modes that depends on an unknown parameter. We will study the components of the model and their restrictions and propose a scheme to solve the problem in which it is possible to determine (adaptive) policies that maximize a suitable discounted reward criterion using standard dynamic programming techniques in combination with discrete estimation methods for the unknown parameter. Finally, we develop a numerical example to illustrate our results with a particular case of the method of minimum least square error approximation. Full article

(This article belongs to the Special Issue Application of Optimal Control and Game Theory to the Problem of Resource Management)

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18 pages, 325 KiB

Open AccessArticle

Solvability of Sequential Fractional Differential Equation at Resonance

by Ahmed Salem and Lamya Almaghamsi

Mathematics 2023, 11(4), 1044; https://doi.org/10.3390/math11041044 - 18 Feb 2023

Cited by 3 | Viewed by 889

Abstract

The sequential fractional differential equations at resonance are introduced subject to three-point boundary conditions. The emerged fractional derivative operators in these equations are based on the Caputo derivative of order that lies between 1 and 2. The vital target of the current contribution [...] Read more.

The sequential fractional differential equations at resonance are introduced subject to three-point boundary conditions. The emerged fractional derivative operators in these equations are based on the Caputo derivative of order that lies between 1 and 2. The vital target of the current contribution is to investigate the existence of a solution for the boundary value problem by using the coincidence degree theory due to Mawhin which is basically depending on the Fredholm operator with index zero and two continuous projectors. An example is given to illustrate the deduced theoretical results. Full article

(This article belongs to the Section Difference and Differential Equations)

28 pages, 4975 KiB

Open AccessArticle

Magnetohydrodynamic Bioconvective Flow of Williamson Nanofluid over a Moving Inclined Plate Embedded in a Porous Medium

by Amir Abbas, Radhika Khandelwal, Hafeez Ahmad, Asifa Ilyas, Liaqat Ali, Kaouther Ghachem, Walid Hassen and Lioua Kolsi

Mathematics 2023, 11(4), 1043; https://doi.org/10.3390/math11041043 - 18 Feb 2023

Cited by 8 | Viewed by 1339

Abstract

Research interest in nanotechnology is growing due to its diversified engineering and medical applications. Due to the importance of bioconvection in biotechnology and various biological systems, scientists have made significant contributions in the last ten years. The present study is focusing on the [...] Read more.

Research interest in nanotechnology is growing due to its diversified engineering and medical applications. Due to the importance of bioconvection in biotechnology and various biological systems, scientists have made significant contributions in the last ten years. The present study is focusing on the investigation of the magnetohydrodynamics (MHD) bioconvective heat transfer of a Williamson nanofluid past an inclined moving plate embedded in a porous medium. The partial differential equations governing the considered configuration are established, then transformed into ordinary differential equations using suitable similarity transformations. The variables corresponding to the velocity, temperature, nanoparticle volume fraction, and density of motile micro-organisms along with their gradients, are computed using the bvp4c-MATLAB built-in numerical solver. Results showed the rising of the buoyancy ration parameter leads to an increase in the flow velocity. It has been also observed that the flow intensity becomes more important with an increase in the Weissenberg number, and the opposite occurs with an increase in the bioconvective Rayleigh number. As an effect of the Brownian motion, a random fluid particle’s motion is encountered. Full article

(This article belongs to the Special Issue Advanced Numerical and Computational Methods for Engineering and Applied Mathematical Problems)

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10 pages, 284 KiB

Open AccessArticle

On Modulated Lacunary Statistical Convergence of Double Sequences

by María del Pilar Romero de la Rosa

Mathematics 2023, 11(4), 1042; https://doi.org/10.3390/math11041042 - 18 Feb 2023

Cited by 2 | Viewed by 965

Abstract

In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function f (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this paper, we will [...] Read more.

In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function f (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this paper, we will explore such a structure in the framework of lacunary statistical convergence for double sequences and discover that such structure remains true for lacunary compatible modulus functions. Thus, we continue the work of Hacer Şenül, Mikail Et and Yavuz Altin, and we fully solve some questions posed by them. Full article

(This article belongs to the Section Mathematical Physics)

20 pages, 592 KiB

Open AccessArticle

A Blockwise Empirical Likelihood Test for Gaussianity in Stationary Autoregressive Processes

by Chioneso S. Marange, Yongsong Qin, Raymond T. Chiruka and Jesca M. Batidzirai

Mathematics 2023, 11(4), 1041; https://doi.org/10.3390/math11041041 - 18 Feb 2023

Viewed by 965

Abstract

A new and simple blockwise empirical likelihood moment-based procedure to test if a stationary autoregressive process is Gaussian has been proposed. The proposed test utilizes the skewness and kurtosis moment constraints to develop the test statistic. The test nonparametrically accommodates the dependence in [...] Read more.

A new and simple blockwise empirical likelihood moment-based procedure to test if a stationary autoregressive process is Gaussian has been proposed. The proposed test utilizes the skewness and kurtosis moment constraints to develop the test statistic. The test nonparametrically accommodates the dependence in the time series data whilst exhibiting some useful properties of empirical likelihood, such as the Wilks theorem with the test statistic having a chi-square limiting distribution. A Monte Carlo simulation study shows that our proposed test has good control of type I error. The finite sample performance of the proposed test is evaluated and compared to some selected competitor tests for different sample sizes and a variety of alternative applied distributions by means of a Monte Carlo study. The results reveal that our proposed test is on average superior under the log-normal and chi-square alternatives for small to large sample sizes. Some real data studies further revealed the applicability and robustness of our proposed test in practice. Full article

(This article belongs to the Special Issue Nonparametric Statistical Methods and Their Applications)

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22 pages, 980 KiB

Open AccessArticle

Analysis of Multi-Server Queueing System with Flexible Priorities

by Konstantin Samouylov, Olga Dudina and Alexander Dudin

Mathematics 2023, 11(4), 1040; https://doi.org/10.3390/math11041040 - 18 Feb 2023

Cited by 2 | Viewed by 2486

Abstract

In this paper, a multi-server queueing system providing service to two correlated flows of requests was considered. Non-preemptive priority was granted to one flow via the preliminary delay of requests in the intermediate buffers with different rates of extracting from the buffers. Customers’ [...] Read more.

In this paper, a multi-server queueing system providing service to two correlated flows of requests was considered. Non-preemptive priority was granted to one flow via the preliminary delay of requests in the intermediate buffers with different rates of extracting from the buffers. Customers’ impatience during waiting in the intermediate and main buffers was taken into account. The possibility of the use of the results of the mathematical analysis for managerial goals is numerically illustrated. Full article

(This article belongs to the Special Issue Advances in Queueing Theory)

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21 pages, 2594 KiB

Open AccessArticle

Economic Order Quantity for Growing Items with Mortality Function under Sustainable Green Breeding Policy

by Amir Hossein Nobil, Erfan Nobil, Leopoldo Eduardo Cárdenas-Barrón, Dagoberto Garza-Núñez, Gerardo Treviño-Garza, Armando Céspedes-Mota, Imelda de Jesús Loera-Hernández and Neale R. Smith

Mathematics 2023, 11(4), 1039; https://doi.org/10.3390/math11041039 - 18 Feb 2023

Cited by 6 | Viewed by 1314

Abstract

Determining the optimal slaughter age of fast-growing animals regarding the mortality rates and breeding costs plays an important and major role for companies that benefit from their meat. Additionally, the effects of carbon dioxide (CO₂) emissions during the growth cycle of [...] Read more.

Determining the optimal slaughter age of fast-growing animals regarding the mortality rates and breeding costs plays an important and major role for companies that benefit from their meat. Additionally, the effects of carbon dioxide (CO₂) emissions during the growth cycle of animals are a significant concern for governments. This study proposes an economic order quantity (EOQ) for growing items with a mortality function under a sustainable green breeding policy. It assumes that CO₂ production is a practical polynomial function that depends on the age of the animals as well as the mortality function. The aim of the model is to determine the optimal slaughter age and the optimal number of newborn chicks, purchased from the supplier, to minimize the total costs. We propose an analytical approach, with five simple steps, to find the optimal solutions. Finally, we provide a numerical example and some model management insights to help practitioners in this area. Full article

(This article belongs to the Special Issue Mathematical Programming, Optimization and Operations Research)

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13 pages, 398 KiB

Open AccessArticle

Regional Consensus Control for Multi-Agent Systems with Actuator Saturation

by Yueyuan Zhang, Yong Qin, Jun Huang, Lin Yang, Tianjiang Zheng and Qingyuan Li

Mathematics 2023, 11(4), 1038; https://doi.org/10.3390/math11041038 - 18 Feb 2023

Viewed by 889

Abstract

This paper considers the regional consensus problem for multi-agent systems with actuator saturation. By utilizing the theory of convex set, a novel multiple nonlinear feedback control protocol is presented, which can effectively reduce the conservatism in dealing with saturated nonlinear input. In order [...] Read more.

This paper considers the regional consensus problem for multi-agent systems with actuator saturation. By utilizing the theory of convex set, a novel multiple nonlinear feedback control protocol is presented, which can effectively reduce the conservatism in dealing with saturated nonlinear input. In order to obtain a larger estimate on the domain of consensus, the composite Laplacian quadratics function is constructed to derive sufficient conditions for the consensus of multi-agent systems. In addition, an alternative convex hull representation is employed to further enlarge the above-mentioned domain of consensus. Finally, a numerical simulation case study illustrates the validity as well as the superiority of the proposed approaches. Full article

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Mathematics, Volume 11, Issue 4 (February-2 2023) – 278 articles

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